{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WPQ5UYD3PQUKAC5FCMZ7DHSWAT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ae8d377fe15f6140c456c3a3f41c4f7c31ba3ebc8ba558de5f5e8f7f139586b2","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-03-14T15:10:56Z","title_canon_sha256":"c09e224a7b733519f5fea4eb85a78eb5223c1416f19d259f3bdc3aab2ce9e869"},"schema_version":"1.0","source":{"id":"math-ph/0703046","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0703046","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0703046v2","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0703046","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"WPQ5UYD3PQUK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WPQ5UYD3PQUKAC5F","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WPQ5UYD3","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d95a2d907f51719832066b8b298b5b8872c78b550d5fc7c6ec8aa1b073aa5a35","target":"graph","created_at":"2026-05-18T01:38:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider diffusion type equations with a distributed order derivative in the time variable. This derivative is defined as the integral in $\\alpha$ of the Caputo-Dzhrbashian fractional derivative of order $\\alpha \\in (0,1)$ with a certain positive weight function. Such equations are used in physical literature for modeling diffusion with a logarithmic growth of the mean square displacement. In this work we develop a mathematical theory of such equations, study the derivatives and integrals of distributed order.","authors_text":"Anatoly N. Kochubei","cross_cats":["math.AP","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2007-03-14T15:10:56Z","title":"Distributed Order Calculus and Equations of Ultraslow Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0703046","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:04b712d0db86ca12b336aa0097b969753f9e0ef03d877b3a29221b5ad4d882b8","target":"record","created_at":"2026-05-18T01:38:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ae8d377fe15f6140c456c3a3f41c4f7c31ba3ebc8ba558de5f5e8f7f139586b2","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-03-14T15:10:56Z","title_canon_sha256":"c09e224a7b733519f5fea4eb85a78eb5223c1416f19d259f3bdc3aab2ce9e869"},"schema_version":"1.0","source":{"id":"math-ph/0703046","kind":"arxiv","version":2}},"canonical_sha256":"b3e1da607b7c28a00ba51333f19e5604d069d77dc00715ccc8f0a6c5daf58d98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3e1da607b7c28a00ba51333f19e5604d069d77dc00715ccc8f0a6c5daf58d98","first_computed_at":"2026-05-18T01:38:30.861073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:30.861073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ds+2ug4W/s3dXvGmLbrbm7y/BZfFxO2SLSeUX++9fr0DB9qQNamWdK3VjknjPOfJbwiWiMuUgYy6HV1+yyEiAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:30.861514Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0703046","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04b712d0db86ca12b336aa0097b969753f9e0ef03d877b3a29221b5ad4d882b8","sha256:d95a2d907f51719832066b8b298b5b8872c78b550d5fc7c6ec8aa1b073aa5a35"],"state_sha256":"a34cb2c1412d6e9bb3cebdcb45efb72977d9280763df51c614516030119f24c2"}